I'm not sure but I speculate that it's at least in part because of the low population as a state itself. Like I mentioned, ABQ isn't super populated and it's our only "major city". If the entire state was sending people there for simple procedures like that they wouldn't have the staff or means to manage it. In Texas they have a few major cities which are way more populated than anywhere here. If you get sent to the city here in New Mexico it was for something major, not something fairly simple like an abortion. At least to my knowledge/experience.
I have had to go to the city for medical stuff before because obviously small towns still won't have the equipment and access to everything we need for every circumstance but I feel like even small towns here have a pretty good ability to treat patients without having to send them elsewhere. Especially for out-patient procedures.